Accession Number : AD0701068

Title :   ON THE SOLUTIONS OF CERTAIN INTEGRAL-LIKE OPERATOR EQUATIONS, EXISTENCE, UNIQUENESS AND DEPENDENCE THEOREMS.

Descriptive Note : Research rept.,

Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ELECTRONIC SCIENCES LAB

Personal Author(s) : Neustadt,Lucien W.

Report Date : FEB 1970

Pagination or Media Count : 58

Abstract : Equations of the form x = Tx are studied, where x is a continuous, finite-dimensional vector-valued function defined on a compact interval, and T is an operator from a set in the linear space of all such functions into this space. Under suitable assumptions - which essentially assert that the operator T is, in some sense, integral-like--local existence, continuation and uniqueness theorems are proved, which are very analogous to those for ordinary differential equations. Further theorems are proved covering the dependence of x on T which generalize well-known continuous and differentiable dependence theorems for ordinary differential equations. The general results are applied to ordinary differential equations, Volterra integral equations, and functional differential equations. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, *DIFFERENTIAL EQUATIONS), (*INTEGRAL EQUATIONS, THEOREMS), VECTOR SPACES, CONVEX SETS, TOPOLOGY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE